In the function:
[tex]y=x^2+10x+15[/tex]
the coefficients are:
a = 1
b = 10
c = 15
Then, b/2 = 10/2 = 5. Computing the square of x and b/2, we get:
[tex](x+5)^2=x^2+2\cdot x\cdot5+5^2=x^2+10x+25[/tex]
We can see that the first two terms coincide with the previous function, then we need to add and subtract 25 to that function to complete the square, as follows:
[tex]\begin{gathered} y=x^2+10+15 \\ y=x^2+10+15+25-25 \\ y=(x^2+10+25)+(15-25) \\ y=(x+5)^2-10 \end{gathered}[/tex]
Solving the equation:
[tex]\begin{gathered} (x+5)^2-10=0 \\ (x+5)^2=0+10 \\ (x+5)^2=10 \\ x+5=\sqrt[]{10} \\ This\text{ equation has 2 solutions:} \\ x_1=\sqrt[]{10}-5 \\ Or \\ x_2=-\sqrt[]{10}-5 \end{gathered}[/tex]
